We perform a numerical test of a relativistic heavy quark(RHQ) action, recently proposed by Tsukuba group, in quenched lattice QCD at $asimeq 0.1$ fm. With the use of the improvement parameters previously determined at one-loop level for the RHQ acti
on, we investigate a restoration of rotational symmetry for heavy-heavy and heavy-light meson systems around the charm quark mass. We focused on two quantities, the meson dispersion relation and the pseudo-scalar meson decay constants. It is shown that the RHQ action significantly reduces the discretization errors due to the charm quark mass. We also calculate the S-state hyperfine splittings for the charmonium and charmed-strange mesons and the $D_s$ meson decay constant. The remaining discretization errors in the physical quantities are discussed.
We calculate charmed meson spectra and decay constants in lattice QCD employing one-loop $O(a)$ improved heavy quark action and axial-vector currents. In quenched simulations at $a sim 0.1$ fm with the plaquette gauge action as well as a renormalizat
ion-group improved one, it is shown that the deviation from the continuum dispersion relation and the violation of space-time symmetry for the pseudoscalar meson decay constants are substantially reduced, once the $O(a)$ improvement is applied. Preliminary results with two flavors of dynamical quarks are also presented.
We review a relativistic approach to the heavy quark physics in lattice QCD by applying a relativistic $O(a)$ improvement to the massive Wilson quark action on the lattice. After explaining how power corrections of $m_Q a$ can be avoided and remainin
g uncertainties are reduced to be of order $(aLambda_{rm QCD})^2$, we demonstrate a determination of four improvement coefficients in the action up to one-loop level in a mass dependent way. We also show a perturbative determination of mass dependent renormalization factors and $O(a)$ improvement coefficients for the vector and axial vector currents. Some preliminary results of numerical simulations are also presented.
